GCSE Maths Practice: volume

Question 1 of 10

This question compares volumes of a cone and a cylinder with the same base and height.

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\( \begin{array}{l}\text{A cone and a cylinder have the same base and height.}\\\text{What fraction of the cylinder's volume is the cone's volume?}\end{array} \)

Choose one option:

Use V = 1/3 × base area × height for cones. Compare with cylinder formula.

The volume of a cone is always one third of a cylinder with the same base and height. Use the formula V = 1/3 × πr^2h for the cone, while the cylinder is V = πr^2h. For example, a cylinder with radius 3 cm and height 6 cm has volume 54π cm^3. The corresponding cone has volume 18π cm^3. Understanding this relationship helps when solving real-life problems such as liquid containers, funnels, and conical tanks. Practice visualizing a cone inside a cylinder to see why the cone occupies exactly one third of the cylinder's space.